How to start a heuristic? Utilizing lower bounds for solving the quadratic assignment problem

The Quadratic Assignment Problem (QAP) is one of the classical combinatorial optimization problems and is known for its diverse applications. The QAP is an NP-hard optimization problem which attracts the use of heuristic or metaheuristic algorithms that can find quality solutions in an acceptable computation time. On the other hand, there is quite a broad spectrum of mathematical programming techniques that were developed for finding the lower bounds for the QAP. This paper presents a fusion of the two approaches whereby the solutions from the computations of the lower bounds are used as the starting points for a metaheuristic, called HC12, which is implemented on a GPU CUDA platform. We perform extensive computational experiments that demonstrate that the use of these lower bounding techniques for the construction of the starting points has a significant impact on the quality of the resulting solutions.

A comprehensive investigation into the performance of genetic algorithm for effective shipyard topological layout

Shipyards have large departments or facilities. It is essential to make an effective topological layout plan since the initial investment cost of these departments is high. Topological layout is an optimization problem and Genetic Algorithm (GA) is generally used in the literature. The selection of effective genetic algorithm approaches and operators are very important to improve the performance of the optimization. This study investigates an effective solution to the shipyard topological layout using a Quadratic Assignment Problem (QAP) model with classic and elitist GA approaches. Besides, genetic operators that have significant effects on exploitation and exploration capabilities are analyzed. Therefore, 126 experiments were run with 13 different operators. The results obtained from the classic and elitist GA approach were evaluated individually and compared with each other. It was observed that the elitist GA approach has a superior performance compared to the classic GA approach. This study is the most comprehensive and practical study on the performance of the GA for topological layout of the shipyard in the literature.

Research on Global Grain Trade Network Pattern and Its Driving Factors

Trading systems are essential in promoting global food security. With the growing proportion of global food consumption obtained through international trade, the global food trade pattern has become increasingly complex over recent years. This study constructed a weighted global grain network using the trade data of 196 countries in 2000 and 2018 to explore the structure and evolution based on the complex network theory. We established that the global grain network was scale-free. There was significant heterogeneity among nodes, and the heterogeneity of the out-degree was greater than that of the in-degree. The global grain network has a significant core-periphery structure, with the United States, Japan, Mexico, Egypt, South Korea, and Colombia as the core countries. Thereafter, by applying the quadratic assignment procedure model to explore the driving factors of the global grain network, we established that geographical distance had a positive impact on the food trade patterns in 2000 and 2018. This differs from the classical gravity model theory. Furthermore, grain trade had significant “boundary effects”; economic gaps, resource endowment, and regional free trade agreements had a positive impact on the evolution of the grain trade network, whereas cultural similarity and political differences had a negative impact on the grain trade network pattern.

Complex Network Analysis of Carbon Emission Transfers under Global Value Chains

Accompanied with the increasing complicated global value chain (GVC) networks is the carbon emission transfers among countries. Utilizing the complex network analysis alongside quadratic assignment procedure (QAP), this paper detects the community structure and influencing forces of the emission transfers under GVCs. The results imply that the bipolar structure of the network transformed gradually to tripolar owing largely to the surging of carbon emissions from China. Evidence on the existence of environmental Kuznets curve (EKC) in the emission transfers from high-income countries to low-income countries, and a U-shape relationship in the transfers in the reverse direction, suggesting that growing carbon emissions from both low- and high-income countries transferred to other high-income countries gradually. Gaps in technology, especially in patent applications, between source and destination countries played an important role therein. JEL: F14, F18, Q56, R15

Thompson Sampling in Heuristic Selection for the Quadratic Assignment Problem

Este trabalho propõe uma Hiper-Heurística (HH) de seleção baseada na abordagem Thompson Sampling (TS) para a solução do Problema Quadrático de Alocação (PQA). O PQA tem como objetivo a alocação de instalações em um conjunto de possíveis localidades já conhecidas, a fim de minimizar o custo total de todas as movimentações entre as instalações. A HH proposta é aplicada na configuração automática de um algoritmo memético, atuando na seleção de uma combinação de heurísticas de baixo nível. Cada combinação envolve a seleção de uma heurística de recombinação, de uma estratégia de busca local e de uma heurística de mutação. O algoritmo foi analisado em 15 instâncias do benchmark Nug e o desempenho da HH é superior àquele obtido por qualquer combinação de heurísticas aplicada de forma isolada, demonstrando a sua eficiência na configuração automática do algoritmo. Os experimentos mostram que o desempenho da TS é afetado pela qualidade do conjunto de heurísticas de baixo nível. A melhor versão da HH obtém a solução ótima em 9 instâncias e o desvio médio percentual da solução ótima (gap), considerando todas as 15 instâncias foi de 8,6%, sendo que os maiores gaps foram encontrados para as três maiores instâncias.

Hyperheuristic Based Migrating Birds Optimization Algorithm for a Fairness Oriented Shift Scheduling Problem

The purpose of this paper is twofold. First, it introduces a new hybrid computational intelligence algorithm to the optimization community. This novel hybrid algorithm has hyperheuristic (HH) neighborhood search movements embedded into a recently introduced migrating birds optimization (MBO) algorithm. Therefore, it is called HHMBO. Second, it gives the necessary mathematical model for a shift scheduling problem of a manufacturing company defined by including the fairness perspective, which is typically ignored especially in manufacturing industry. Therefore, we call this complex optimization problem fairness oriented integrated shift scheduling problem (FOSSP). HHMBO is applied on FOSSP and is compared with the well-known simulated annealing, hyperheuristics, and classical MBO algorithms through extended computational experiments on several synthetic datasets. Experiments demonstrate that the new hybrid computational intelligence algorithm is promising especially for large sized instances of the specific problem defined here. HHMBO has a high exploration capability and is a promising technique for all optimization problems. To justify this assertion, we applied HHMBO to the well-known quadratic assignment problem (QAP) instances from the QAPLIB. HHMBO was up to 14.6% better than MBO on converging to the best known solutions for QAP benchmark instances with different densities. We believe that the novel hybrid method and the fairness oriented model presented in this study will give new insights to the decision-makers in the industry as well as to the researchers from several disciplines.

The Spatial Correlation and Driving Mechanism of Wood-Based Products Trade Network in RCEP Countries

Clarifying the spatial correlation and driving mechanism of wood-based products trade network is conducive to promoting the Regional Comprehensive Economic Partnership (RCEP) to a higher level. Firstly, we explored the characteristics of spatial correlation and evolution tendency of raw material-type wood-based products trade network (TN-WFPM) and product-type wood-based products trade network (TN-WFPP) from the overall characteristics, centrality, and node coreness of the networks according to social network analysis method. Then we analyzed the driving mechanism of the spatial correlation according to the quadratic assignment procedure (QAP). The results show that, compared with TN-WFPM, the density, reciprocity, and agglomeration of the TN-WFPP are relatively stronger. The centrality and evolution characteristics of RCEP countries are different in the networks. The coreness of China and Thailand in the TN-WFPP has always been in the top two, while the coreness of China, Japan, and Korea has increased significantly and China has been the top since 2010 in the TN-WFPM. Factors like cultural distance, forest resource endowment, forest certification area, economic scale, economic distance, and free trade agreements (FTA) have significant impacts on the spatial correlation of wood-based products trade among RCEP countries. Furthermore, the impacts of different factors on the two kinds of networks are heterogeneous.

Garden optimization problems for benchmarking quantum annealers

We benchmark the 5000+ qubit system coupled with the Hybrid Solver Service 2 released by D-Wave Systems Inc. in September 2020 by using a new class of optimization problems called garden optimization problems known in companion planting. These problems are scalable to an arbitrarily large number of variables and intuitively find application in real-world scenarios. We derive their QUBO formulation and illustrate their relation to the quadratic assignment problem. We demonstrate that the system and the new hybrid solver can solve larger problems in less time than their predecessors. However, we also show that the solvers based on the 2000+ qubit system sometimes produce more favourable results if they can solve the problems.